enrolled actuaries basic examination ea-1 · exam ea-1 spring 2014 - 11 - go on to next page data...

an annuity. On this examination the symbol “x

l ” will be used

AMERICAN SOCIETY OF PENSION PROFESSIONALS & ACTUARIES JOINT BOARD FOR THE ENROLLMENT OF ACTUARIES SOCIETY OF ACTUARIES

Enrolled Actuaries Basic Examination

EA-1

Date: Tuesday, May 6, 2014 Time: 8:30 a.m. – 11:00 a.m.

INSTRUCTIONS TO CANDIDATES

1. Write your candidate number here ____________. Your name must not appear.

2. Do not break the seal of this book until the supervisor tells you to do so.

3. Special conditions generally applicable to all questions on this examination are found at the front of this book.

4. On this examination the symbol “ a ” will be used to represent to represent the number of lives at age x.

5. This examination consists of 32 multiple-choice questions worth a total of 100 points. The point value for each question is shown in parentheses at the beginning of the question.

6. Your score will be based on the point values of questions that you answer correctly. No credit will be given for omitted answers and no credit will be lost for wrong answers; hence, you should answer all questions even those for which you have to guess.

7. A separate answer sheet is inside the front cover of this book. During the time allotted for this examination, record all your answers on side 2 of the answer sheet. NO ADDITIONAL TIME WILL BE ALLOWED FOR THIS PURPOSE. No credit will be given for anything indicated in the examination book but not transferred to the answer sheet. Failure to stop writing or coding your answer sheet after time is called will result in the disqualification of your answer sheet or further disciplinary action.

8. Five answer choices are given with each question, each answer choice being identified by a key letter (A to E). For each question, blacken the oval on the answer sheet that corresponds to the key letter of the answer choice that you select.

9. Use a soft-lead pencil to mark the answer sheet. To facilitate

correct mechanical scoring, be sure that, for each question, your pencil mark is dark and completely fills only the intended oval. Make no stray marks on the answer sheet. If you have to erase, do so completely.

10. Do not spend too much time on any one question. If a question seems too difficult, leave it and go on.

11. While every attempt is made to avoid defective questions, sometimes they do occur. If you believe a question is defective, the supervisor or proctor cannot give you any guidance beyond the instructions on the exam booklet.

12. Clearly indicated answer choices in the test book can be an

aid in grading examinations in the unlikely event of a lost answer sheet.

13. Use the blank portions of each page for your scratch work. Extra blank pages are provided at the back of the examination book.

14. When the supervisor tells you to do so, break the seal on the book and remove the answer sheet.

On the front of the answer sheet, space is provided to write and code candidate information. Complete the information requested by printing in the squares and blackening the circles (one in each column) corresponding to the letters or numbers printed. For each empty box blacken the small circle immediately above the “A” circle. Fill out the boxes titled:

(a) Name

(Include last name, first name and middle initial) (b) Candidate Number

(Candidate/Eligibility Number, use leading zeros if needed to make it a five digit number)

(c) Test Site Code

(The supervisor will supply the number.) (d) Examination Part

(Code the examination that you are taking by blackening the circle to the left of "Exam EA-1")

(e) Booklet Number

(The booklet number can be found in the upper right-hand corner of this examination book. Use leading zeros if needed to make it a four digit number.)

In the box titled “Complete this section only if instructed to do so”, fill in the circle to indicate if you are using a calculator and write in the make and model number. In the box titled “Signature and Date” sign your name and write today's date. If the answer sheet is not signed, it will not be graded. Leave the boxes titled “Test Code” and “Form Code” blank.

On the back of the answer sheet fill in the Booklet Number in the space provided.

15. After the examination, the supervisor will collect this book and the answer sheet separately. DO NOT ENCLOSE THE ANSWER SHEET IN THE BOOK. All books and answer sheets must be returned. THE QUESTIONS ARE CONFIDENTIAL AND MAY NOT BE TAKEN FROM THE EXAMINATION ROOM.

Exam EA-1

EA-1 Spring 2014 Answer Key

Updated March 3, 2014 Question Points Solution

1 E 2 B 3 B 4 D 5 B 6 D 7 B 8 B 9 A 10 C 11 C 12 B 13 B 14 C 15 D 16 B 17 B 18 C 19 C 20 C 21 C 22 B 23 A 24 C 25 B 26 B 27 C 28 B 29 B 30 C 31 C 32 D

CONDITIONS GENERALLY APPLICABLE TO ALL EA-1 EXAMINATION QUESTIONS

If applicable, the following conditions should be considered a part of the data for each question, unless otherwise stated or implied: (1) The normal retirement age is 65. (2) Retirement pensions commence at normal retirement age and are paid monthly for life at the

beginning of each month. (3) There are no pre-retirement death or disability benefits. (4) Actuarial equivalence is based on the mortality table and interest rate assumed for funding

purposes. (5) Interest rates that are compounded more frequently than annually are expressed as nominal rates. (6) Where multiple lives are involved, future lifetimes are assumed to be independent of each other. (7) The term “gross single premium” is equivalent to “contract single premium;” the term “net single

premium” is equivalent to “single benefit premium;” the term “gross annual premium” is equivalent to “annual contract premium;” the term “net annual premium” is equivalent to “annual benefit premium.”

(8) There are no policy loans in effect. (9) For a bond, the face amount and the redemption value are the same. (10) Interest rate equals yield rate. (11) The term “duration” means “Macaulay duration”.

Exam EA-1 Spring 2014 - 1 - GO ON TO NEXT PAGE

Data for Question 1 (4 points) Terms of an annuity:

Payments are made annually at the end of each year. Amount of payments $1,500 per year, payable for the first n years $2,500 per year, payable for the next m years $3,500 per year, payable for the next 2n years

Selected annuity values:

8.559

9.818

0.215

n

m

m

a

a

v

=

=

=

X = present value of the annuity.

Question 1 In what range is X? (A) Less than $18,000 (B) $18,000 but less than $19,500 (C) $19,500 but less than $21,000 (D) $21,000 but less than $22,500 (E) $22,500 or more


USE THIS PAGE FOR YOUR SCRATCH WORK

EXTRA BLANK PAPER IS PROVIDED AT THE END OF THE EXAM BOOK


Data for Question 2 (4 points) The current basic life table follows the formula:

1000(110 )xl x= −

To reflect mortality improvement, the applicable rates t years hence are as follows:

( )0.95 , 0,1, 2,tPROJECTED BASIC

x xq q t= =

Smith, now age 50, is to receive a 3-year annuity-immediate of $10,000 per year, payable annually. Interest: 5% per year, compounded annually. X = the single premium for this annuity.



Data for Question 3 (3 points) From a 1-year select and ultimate mortality table:

[ ]

0.96

0.75

x

xx

p

q q

=

=

Interest rate: 5.0% per year, compounded annually.

0.60xA =

X = the single premium for a $1 per year annuity-due, payable annually, to [x] for life.

Question 3 In what range is X? (A) Less than $8.45 (B) $8.45 but less than $8.55 (C) $8.55 but less than $8.65 (D) $8.65 but less than $8.75 (E) $8.75 or more


Data for Question 4 (3 points)

10 90.50a a− =

( )( )

2

19 18

3

9 8

s s

s s

−=

−X

Question 4 In what range is X? (A) Less than 1.50 (B) 1.50 but less than 1.70 (C) 1.70 but less than 1.90 (D) 1.90 but less than 2.10 (E) 2.10 or more


Data for Question 5 (3 points) A survival function is defined as follows:

S x( ) = 1− x

250

0 ≤ x < 25

ℓx = 1000 100 − x( ) x ≥ 25

1030 10 q=X



Data for Question 6 (4 points) Smith buys a 10-year decreasing annuity-immediate with annual payments of 10, 9, 8, … , 1. On the same date, Smith buys a perpetuity-immediate with annual payments. For the first 11 years, payments of the perpetuity-immediate are 1, 2, 3, … , 11. After year 11, payments remain constant at 11. At an annual effective interest rate of i, both annuities have a present value equal to X.

Question 6 In what range is X? (A) Less than $26 (B) $26 but less than $28 (C) $28 but less than $30 (D) $30 but less than $32 (E) $32 or more


Data for Question 7 (3 points) Smith takes out a $200,000 loan to be repaid in equal monthly installments over 30 years. The first payment is due one month after the loan is made. Immediately after the 60th payment is made, Smith makes an additional payment of $50,000 and refinances the remaining balance in equal monthly installments over 10 years, with the first payment due at the beginning of the month following the refinancing. Interest rate of original loan: 6.0% per year, compounded monthly. Interest rate of refinanced amount: 5.0% per year, compounded monthly. X = the monthly payment amount after refinancing.



Data for Question 8 (2 points) In a double-decrement table, you are given the following:

( )

( )

( )

11

11 |

2

0.3333

0.2292

0.1250

x

x

x

q

q

q

+ =

=

=

Question 8 In what range is (1)

xq ?

(A) Less than 0.1000 (B) 0.1000 but less than 0.2000 (C) 0.2000 but less than 0.3000 (D) 0.3000 but less than 0.4000 (E) 0.4000 or more


Data for Question 9 (2 points) Terms of a bond:

Face value $1,000 Coupon rate 6.0% annual, payable at end of year Call date Any time between 10 and 15 years after purchase date Redemption amount Par

=X the maximum amount a purchaser would pay to guarantee a yield rate of at least 5.0% per annum.



Data for Question 10 (3 points) Deaths are uniformly distributed over each year of age. For a given integer age x: xq = 0.400

1xq + = 0.500

0.5xq +=X



Data for Question 11 (4 points) Selected commutation functions:

x xN

64 294,298 65 263,044 66 234,434 67 208,299 68 184,481

Interest rate: 7.0% per year, compounded annually. X =

64:65:2a



Data for Question 12 (3 points) Pension fund information:

Date Fund balance Contribution Distribution 01/01/2013 $100,000 − − 03/31/2013 − − $10,000 04/01/2013 $100,000 − − 06/30/2013 − $50,000 $10,000 07/01/2013 $150,000 − − 09/30/2013 − − $10,000 10/01/2013 $140,000 − − 12/31/2013 − − $10,000 01/01/2014 $130,000 − −

X = the dollar-weighted rate of return in 2013.

Question 12 In what range is X? (A) Less than 17.9% (B) 17.9% but less than 18.9% (C) 18.9% but less than 19.9% (D) 19.9% but less than 20.9% (E) 20.9% or more


Data for Question 13 (3 points) Selected values:

x xe

63 9.5

64 9.0

65 8.5

Question 13 In what range is 2 63 ?q



Data for Question 14 (2 points) Terms of a bond:

Face amount $1,000 Term to maturity 3 years Coupon rate 6.0% per year, payable annually

Term structure of interest rates: Term (years) Annual spot interest rate 1 7.0% 2 8.0% 3 9.0% X = the value of the bond.



Data for Question 15 (3 points) Smith pays $950 for an investment that returns $500 at the end of year 3, and $700 at the end of year 4. The price is based on a 2-year spot rate of 5.0% and a 4-year spot rate of 7.0%. X = the year 3 forward rate (i.e., the 2-year deferred, 1-year spot rate).

Question 15 In what range is X? (A) Less than 7.1% (B) 7.1% but less than 7.8% (C) 7.8% but less than 8.5% (D) 8.5% but less than 9.2% (E) 9.2% or more


Data for Question 16 (3 points) A service table has three decrements: death (d), withdrawal (w), retirement (r). Deaths are uniformly distributed over each year of age. All retirements occur at the start of the year. All withdrawals occur at mid-year. Under the associated single-decrement tables, rates at age 63 are:

( )

( )

( )

63

63

63

0.020

0.125

0.200

d

w

r

q

q

q

′ =

′ =

′ =

Question 16 In what range is ( )

63dq ?



Data for Question 17 (3 points) Data for a single premium life insurance policy:

Age at issue 40 Benefit $10,000 payable at end of year of death

If death occurs before age 50, an additional benefit equal to 50% of the single premium accumulated with interest at 5.0%, compounded annually, is payable at the end of the year of death. Selected actuarial values:

40

5 40

5 45

0.31549

0.71823

0.71230

A

E

E

===

Interest rate: 5.0% per year, compounded annually.

Question 17 In what range is the net single premium? (A) Less than $3,300 (B) $3,300 but less than $3,700 (C) $3,700 but less than $4,100 (D) $4,100 but less than $4,500 (E) $4,500 or more


Data for Question 18 (4 points) Smith (age 55) is entitled to a pension benefit at the beginning of each month of $750 for life commencing immediately. Smith elects a “Social Security level income option” under a pension plan such that the total of Smith’s monthly income from the pension plan plus the amount Smith receives from Social Security remains level for Smith’s lifetime. Smith’s monthly Social Security benefit is $1,400, commencing at age 62. Selected actuarial values:

X = the monthly benefit payable to Smith from the pension plan from age 55 to age 62 under

the Social Security level income option.



Data for Question 19 (4 points) Terms of a mortgage:

Interest rate 4.50% per year, convertible monthly Payments Level monthly, payable at the end of each month Term 20 years

X = the modified duration of the mortgage.



Data for Question 20 (3 points) Employee Smith earns an annual salary in 2014 of $50,000. Smith’s assumed salary increases: 3% each year, beginning 1/1/2015. At the end of each year, beginning with 2014, 5% of Smith’s annual salary is deposited into a fund earning an annual rate of interest of 6%. It is assumed that Smith will remain employed until 2035. X = the projected amount in Smith’s fund on 1/1/2035.



Data for Question 21 (4 points) An annuity-immediate is issued to three lives, all of whom are age 64 at issue. Amount paid $500 per year if exactly one annuitant is alive

$750 per year if exactly two annuitants are alive $1,000 per year if exactly three annuitants are alive

Selected annuity values: 64a = 25.00

64:64a = 15.00

64:64:64a = 10.00

X = the net single premium for this annuity.



Data for Question 22 (2 points) Assume deaths are uniformly distributed over each year of age.

60

61

0.0200

0.0220

q

q

==

1.5 60q=X



Data for Question 23 (3 points) Terms of a loan:

Repayment period 20 years Annual repayments $100, with first payment made at the end of the first year Interest rate 5.0% per year, compounded annually

3.0% of the interest portion of each annual repayment is applied to the expenses for the loan. X = the sum of expenses incurred over the life of the loan.



Data for Question 24 (4 points) Smith (age 60) is scheduled to receive an annuity-immediate of $10,000 per year, payable annually for life and continuing for 10 years after Smith’s death.

60 12.70a =

Interest rate: 5% per year, compounded annually. X = the present value of this annuity.



Data for Question 25 (3 points) The following actuarially equivalent annuities are available to Smith:

1. Monthly payments of $100 for Smith’s life

2. Monthly payments of $94 for Smith’s life, with monthly payments of $47 continuing for the life of Smith’s surviving spouse

3. Monthly payments of X for Smith’s life, with monthly payments of

0.75X continuing for the life of Smith’s surviving spouse

Question 25 In what range is X? (A) Less than $90.52 (B) $90.52 but less than $91.52 (C) $91.52 but less than $92.52 (D) $92.52 but less than $93.52 (E) $93.52 or more


Data for Question 26 (3 points) Smith, age x, purchases a 3-year term insurance policy of $1,000 with death benefit payable at the end of the year of death. Selected actuarial values: xq = 0.20

1xq + = 0.25

2xq + = 0.30

Current price of $100 zero-coupon bond maturing in n years: n Price 1 $97.00 2 $93.00 3 $89.00 X = the net single premium for this insurance policy.



Data for Question 27 (3 points) From a 1-year select and ultimate mortality table:

[ ]

70

7070

9.8269

1.013

a

p p

==

Question 27 In what range is [ ]70 ?a



Data for Question 28 (3 points) Smith is 55, Jones is 45, and Brown is 40. The underlying mortality table is assumed to be the same for all three individuals. There is a 40% probability that Smith and Brown will both be alive in 15 years. There is a 44% probability that Jones will die before age 70. X = the probability that Brown will die before age 45.



Data for Question 29 (3 points) On 1/1/2014, a company purchases one-year corporate bonds where the expected proceeds are $2,000,000 on 12/31/2014. The bonds have the following terms:

Each bond is redeemable at par value of $1,000. Coupon rate: 8% per year, payable end-of-year The probability of default during the year on each bond is 6.0%. If a bond defaults, the recovery value at year-end is $600. The default of any bond is independent of the default of any other bond. X = the total number of bonds to be purchased on 1/1/2014.

Question 29 In what range is X? (A) Less than 1,900 (B) 1,900 but less than 1,905 (C) 1,905 but less than 1,910 (D) 1,910 but less than 1,915 (E) 1,915 or more


Data for Question 30 (3 points) A loan of $100,000 is to be amortized over 20 years by level annual payments at the beginning of each year. Spot rates on the yield curve are as follows:

Years Rate Less than 5 4.0% 5 through 9 6.0% 10 and over 6.5%

X = the annual amortization amount.




ℓ[x]+t

= 100 − x − t

2, 0 ≤ t ≤ 6

ℓx+t = 103− x − t, t > 6

X = the probability that a life now age 52, who entered the selection period 2 years ago, will die

between ages 54 and 58.


Exam EA-1 Spring 2014 - 63 - STOP


15 25p = 0.8108

2515 15 q = 0.2027

10 55q = 0.2222

2530 10 q=X


**END OF EXAMINATION**

enrolled actuaries basic examination ea-1 · exam ea-1 spring 2014 - 11 - go on to next page data...

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